Solve for $x$ and $y$ using elimination. ${3x-5y = 25}$ ${-3x+3y = -27}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the top and bottom equations together. $-2y = -2$ $\dfrac{-2y}{{-2}} = \dfrac{-2}{{-2}}$ ${y = 1}$ Now that you know ${y = 1}$ , plug it back into $\thinspace {3x-5y = 25}\thinspace$ to find $x$ ${3x - 5}{(1)}{= 25}$ $3x-5 = 25$ $3x-5{+5} = 25{+5}$ $3x = 30$ $\dfrac{3x}{{3}} = \dfrac{30}{{3}}$ ${x = 10}$ You can also plug ${y = 1}$ into $\thinspace {-3x+3y = -27}\thinspace$ and get the same answer for $x$ : ${-3x + 3}{(1)}{= -27}$ ${x = 10}$